Nuprl Lemma : decidable__existse-between1
∀es:EO. ∀e1,e2:E.
∀[P:{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ]. ∀e@loc(e1).Dec(P[e]) ⇒ Dec(∃e∈[e1,e2).P[e]) supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
existse-between1: ∃e∈[e1,e2).P[e],
alle-at: ∀e@i.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
alle-at_wf,
Id_wf,
es-loc_wf,
es-E_wf,
decidable_wf,
equal_wf,
event_ordering_wf,
decidable__existse-before,
es-le_wf,
decidable__and,
decidable__es-le,
es-locl_wf,
es-le-loc,
not_wf,
exists_wf
\mforall{}es:EO. \mforall{}e1,e2:E.
\mforall{}[P:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e]) {}\mRightarrow{} Dec(\mexists{}e\mmember{}[e1,e2).P[e]) supposing loc(e2) = loc(e1)
Date html generated:
2015_07_17-AM-08_47_33
Last ObjectModification:
2015_01_27-PM-02_28_06
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